Math Problem Statement

Graph the line. y=3x

Solution

The equation given is y=3xy = 3x. This is a linear equation in slope-intercept form, y=mx+by = mx + b, where:

  • m=3m = 3 is the slope of the line.
  • b=0b = 0 is the y-intercept, meaning the line passes through the origin (0,0).

Steps to graph the line:

  1. Plot the y-intercept: The y-intercept is at (0,0).
  2. Use the slope: The slope m=3m = 3 means that for every 1 unit increase in xx, yy increases by 3 units. From the origin, go right 1 unit on the xx-axis and then move up 3 units to the point (1,3).
  3. Draw the line: After plotting these two points, draw a straight line through them.

Would you like me to provide more details or solve another question?

Here are 5 related questions to consider:

  1. What does the slope represent in a linear equation?
  2. How would the graph change if the slope was negative, for example y=3xy = -3x?
  3. How can you determine the slope and y-intercept from any given linear equation?
  4. How do you find the equation of a line from a graph?
  5. How does the equation change if the line is parallel to y=3xy = 3x?

Tip: A slope of 3 means the line rises 3 units vertically for every 1 unit it moves horizontally!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

Slope-intercept form: y = mx + b

Theorems

Slope formula

Suitable Grade Level

Grades 6-8